Odd priest's behind (4)
I believe the answer is:
rump
'behind' is the definition.
('rump' can be a synonym of 'behind')
'odd priest's' is the wordplay.
'odd' becomes 'rum' (I've seen this before).
'priest' becomes 'p' (ecclesiastical abbreviation).
'rum'+'p'='RUMP'
(Other definitions for rump that I've seen before include "historical Parliament" , "Backside" , "Fleshy hindquarters" , "Type of steak" , "Mammal's hind part" .)